(i) A harmonic wave in a stationary medium is represented by `y = a sin (kx – omegat)`. Write the equation of this wave for an observer who is moving in negative `x` direction with constant speed `v_(0)`.
(ii) The Doppler flow meter is a device that measures the speed of blood flow, using transmitting and receiving elements that are placed directly on the skin. The transmitter emits a continuous sound wave whose frequency is `5 M Hz`. When the sound is reflected from the red blood cells, its frequency is changed in a kind of Doppler effect. The cells are moving with the same velocity as the blood. The receiving element detects the reflected sound, and an electronic counter measures its frequency, which is Doppler- shifted relative to the transmitter frequency. From the change in frequency the speed of the blood flow can be determined. Typically, the change in frequency is around `600 Hz` for flow speeds of about `0.1 m//s`. Assume that the red blood cell is directly moving away from the source and the receiver. (a) Estimate the speed of the sound wave in the blood?
(b) A segment of artery is narrowed down by plaque to half the normal cross-sectional area. What will be the Doppler change in frequency due to reflection from the red blood cell in that region?

Answer

(i) `y=a sin [(omega_kv_(0))t-kx]`
(ii) (a) 1700 m/s
(b) 1200 Hz